Fast Magnetic Resonance Imaging (MRI) and Chemical Shift Imaging (CSI) require both high signal to noise ratio (SNR) as well as fast data acquisition. These fast imaging techniques are critical in imaging moving parts of the body such as cardiac imaging, one of the largest growing applications of MRI. The development of partially parallel imaging (PPA) methods such as SENSE and SMASH have made it possible to collect image data 2–3 times faster than before when combined with an optimized phased array coil. A new area is to apply these reduced phase encode methods to CSI which traditionally has been plagued by long acquisition times.
The speed up factors currently available are typically 2 or 3. The demand for faster imaging is so great that the ability to produce speed up factors of 5 or 6 would be huge.
There are also applications where movement is such a problem that faster acquisitions are still not able to produce acceptable results, such as kinetic knee studies. In these cases, the fact that B0 field gradients are used at all makes some applications inconceivable. If we could not only increase the speed up factor of PPA, but also collect data without the use of spatial encoding gradients, the applications would be limitless.
According to present technology, the NMR signal, Sm(kn), received by a coil array element m of the M receive coils, during application of a pulse sequence for the n-th phase encoding step in k-space is given bySm(kn)=∫drρ(r)ei(kn·r)Cm(r),
where kn is the nth spatial encoding k-space trajectory for the spatial dimension r, Cm(r) is the receive coil sensitivity, and ρ(r) represents the magnetization spatial distribution arising from the spin density spatial distribution, the pulse sequence and the transmit excitation profile. This is the standard form of the Fourier transform relating the time domain or k-space signal Sm(kn) to the frequency domain of spatial signal ρ(r). Traditionally in MRI, the encoding function or kernel f(k,r) of this transformation is the exponential function, that is,ƒ(kn,r)=ei(kn·r),where, Sm(kn)=∫drρ(r)ƒ(kn,r)Cm(r)
The k-space trajectory is generated with magnetic field gradients in the x, y or z directions. For 2D imaging, only two orthogonal directions are used with the third direction used for slice selection. Without loss of generality, suppose that for a y-z image, the phase encoding is taken to be in the z-direction. Then after Fourier transformation in the frequency encode direction (y), the above equation in this hybrid space becomes,Sm(y,kn)=∫dzρ(y,z)ei(nΔkzz)Cm(r),
where Δkz is the separation between k-space lines relating to the Field-Of-View (FOV) of the image, n ε[0,N] where N defines the resolution in the phase encode dimension (z).
If k-space is incompletely sampled by skipping phase encode lines, effectively increasing Δkz, then image reconstruction will result in wrapping or fold-over artifacts due to a smaller FOV in the phase encode dimension.
It is well known that if the M-array coil sensitivities are partially orthogonal in the phase encode direction, then the missing phase encode lines can be recovered with proper combination of the resulting wrapped images in the time domain using a technique known as SMASH D. K. Sodickson, W. J. Manning, Simultaneous Acquisition of Spatial Harmonics (SMASH): Fast Imaging with Radiofrequency Coil Arrays, Magn. Reson. Med. 38:591–603 (1997), or unwrapped in the image domain using a technique known as SENSE K. P. Pruessmann, M. Weiger, M. B. Scheidegger, P. Boesiger, SENSE: Sensitivity Encoding for Fast MRI, Magn. Reson. Med. 42:952–962 (1999), using this orthogonal knowledge of the coil sensitivities. The term partially orthogonal is used in the context that the coil sensitivities Cm, at wrapping pixel locations partially differ in their magnitude and/or phase distributions from each other along the phase encode direction.
One example of this would be box functions spanning different spatial locations in the phase encode direction (magnitude partial orthogonality). Another example would be traditional birdcage-field and spiral birdcage fields in which case the transverse B1 phase gives rise to orthogonal B1 in the phase encode direction (phase partial orthogonality).
The SMASH version is explained in the time domain as follows. Suppose, the M-receive coil sensitivities Cm(r) for m ε[0,M], are partially orthogonal in the phase encode direction, z, such thatCm(km,r)=C0ei(kmRz)=C0ei(mΔkzz).
In this simplified case, each receive coil is capable of producing a different order-m of the k-space lines. That is, the coil sensitivity function can be included into the Fourier transform kernel, such thatƒC(kp,r)=ei(kn·r)Cm(kmR,r),Sm(kp)=∫drρ(r)ƒC(kp,r)
For every acquired phase encode line n (n ε N), the p=n+m phase encode line can also be generated without actually acquiring the p-phase encode line of data. Purposely making the missing phase encode lines the p-phase encode lines, all of k-space can be filled in for a reconstructed image with no wrapping artefact. Because the N+M lines are achieved with only N-applications of the pulse sequence, a time saving is achieved by the factor 1/R, where R=M is called the reduction factor. What this also means is that for mε[0,M], M phase encoding steps can be achieved without the use of any gradient phase encoding steps (n=0).
The SENSE version is explained in the image domain as follows. Suppose every Rth phase encode step is skipped producing M-array images with R-fold wrapping. This means that R-pixels along the phase encode direction are superimposed onto one in the wrapped images. For the m-array coil element, the pth pixel value (Smp) is given by the sum of the wrapped pixels each weighted by the m-array coil element sensitivity at the wrapped pixel location, q. This is given by
            S      p      m        =                  ∑                  q          =          1                R            ⁢                        s          q                ⁢                  C          q          m                      ,
or in matrix form,S=sC.
Here S is an M×1 vector, s is a 1×R vector and C is an R×M matrix. The true (unwrapped) pixel values, sq, can be obtained by solving for s.
As mentioned above, with current 4–8 channel receiver MRI systems, the present solutions can only achieve 2–3 fold speed-up factors and also still use B0 field gradient encoding.